7.4m.yushuwu.org

HiddenMarkovModelsinFinanceRecenttitlesintheINTERNATIONALSERIESINOPERATIONSRESEARCH&MANAGEMENTSCIENCEFrederickS.
Hillier,SeriesEditor,StanfordUniversityGass&Assad/ANANNOTATEDTIMELINEOFOPERATIONSRESEARCH:AnInformalHistoryGreenberg/TUTORIALSONEMERGINGMETHODOLOGIESANDAPPLICATIONSINOPERATIONSRESEARCHWeber/UNCERTAINTYINTHEELECTRICPOWERINDUSTRY:MethodsandModelsforDecisionSupportFigueira,Greco&Ehrgott/MULTIPLECRITERIADECISIONANALYSIS:StateoftheArtSurveysReveliotis/REAL-TIMEMANAGEMENTOFRESOURCEALLOCATIONSSYSTEMS:ADiscreteEventSystemsApproachKall&Mayer/STOCHASTICLINEARPROGRAMMING:Models,Theory,andComputationSethi,Yan&Zhang/INVENTORYANDSUPPLYCHAINMANAGEMENTWITHFORECASTUPDATESCox/QUANTITATIVEHEALTHRISKANALYSISMETHODS:ModelingtheHumanHealthImpactsofAntibioticsUsedinFoodAnimalsChing&Ng/MARKOVCHAINS:Models,AlgorithmsandApplicationsLi&Sun/NONLINEARINTEGERPROGRAMMINGKaliszewski/SOFTCOMPUTINGFORCOMPLEXMULTIPLECRITERIADECISIONMAKINGBouyssouetal.
/EVALUATIONANDDECISIONMODELSWITHMULTIPLECRITERIA:SteppingstonesfortheanalystBlecker&Friedrich/MASSCUSTOMIZATION:ChallengesandSolutionsAppa,Pitsoulis&Williams/HANDBOOKONMODELLINGFORDISCRETEOPTIMIZATIONHerrmann/HANDBOOKOFPRODUCTIONSCHEDULINGAxster/INVENTORYCONTROL,2ndEd.
Hall/PATIENTFLOW:ReducingDelayinHealthcareDeliveryJózefowska&Weglarz/PERSPECTIVESINMODERNPROJECTSCHEDULINGTian&Zhang/VACATIONQUEUEINGMODELS:TheoryandApplicationsYan,Yin&Zhang/STOCHASTICPROCESSES,OPTIMIZATION,ANDCONTROLTHEORYAPPLICATIONSINFINANCIALENGINEERING,QUEUEINGNETWORKS,ANDMANUFACTURINGSYSTEMSSaaty&Vargas/DECISIONMAKINGWITHTHEANALYTICNETWORKPROCESS:Economic,Political,Social&TechnologicalApplicationsw.
Benets,Opportunities,Costs&RisksYu/TECHNOLOGYPORTFOLIOPLANNINGANDMANAGEMENT:PracticalConceptsandToolsKandiller/PRINCIPLESOFMATHEMATICSINOPERATIONSRESEARCHLee&Lee/BUILDINGSUPPLYCHAINEXCELLENCEINEMERGINGECONOMIESWeintraub/MANAGEMENTOFNATURALRESOURCES:AHandbookofOperationsResearchModels,Algorithms,andImplementationsHooker/INTEGRATEDMETHODSFOROPTIMIZATIONDawandeetal.
/THROUGHPUTOPTIMIZATIONINROBOTICCELLSFriesz/NETWORKSCIENCE,NONLINEARSCIENCEANDDYNAMICGAMETHEORYAPPLIEDTOTHESTUDYOFINFRASTRUCTURESYSTEMSCai,Sha&Wong/TIME-VARYINGNETWORKOPTIMIZATION*Alistoftheearlypublicationsintheseriesisattheendofthebook*HiddenMarkovModelsinFinanceEditedbyRogemarS.
MamonRobertJ.
ElliottRogemarS.
MamonRobertJ.
ElliottUniversityofWesternOntarioUniversityofCalgaryLondon,CanadaCalgary,CanadaLibraryofCongressControlNumber:2007921976ISBN-10:0-387-71081-7(HB)ISBN-10:0-387-71163-5(e-book)ISBN-13:978-0-387-71081-5(HB)ISBN-13:978-0-387-71163-8(e-book)Printedonacid-freepaper.
c2007bySpringerScience+BusinessMedia,LLCAllrightsreserved.
Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMedia,LLC,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.
Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknoworhereafterdevelopedisforbidden.
Theuseinthispublicationoftradenames,trademarks,servicemarksandsimilarterms,evenifthearenotidentiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.
987654321springer.
comContents1AnExactSolutionoftheTermStructureofInterestRateunderRegime-SwitchingRiskShuWu,YongZeng11.
1Introduction11.
2Anewrepresentationformodelingregimeshift.
31.
3Themodel.
51.
3.
1Twostatevariables51.
3.
2Pricingkernel51.
3.
3Therisk-neutralprobabilitymeasure51.
3.
4Thetermstructureofinterestrates81.
4Atractablespecicationwithexactsolution91.
4.
1Aneregime-switchingmodels91.
5Conclusions.
13References132TheTermStructureofInterestRatesinaHiddenMarkovSettingRobertJ.
Elliott,CraigA.
Wilson152.
1Introduction152.
2TheModel172.
2.
1TheMarkovchain172.
2.
2Theshort-terminterestrate202.
2.
3Thezero-couponbondvalue212.
3Implementation222.
4Results.
252.
5Conclusion30References30VIContents3OnFairValuationofParticipatingLifeInsurancePoliciesWithRegimeSwitchingTakKuenSiu313.
1Introduction313.
2Themodeldynamics333.
3Dimensionreductiontoregime-switchingPDE383.
4Furtherinvestigation.
42References424PricingOptionsandVarianceSwapsinMarkov-ModulatedBrownianMarketsRobertJ.
Elliott,AnatoliyV.
Swishchuk454.
1Introduction454.
2Literaturereview474.
3MartingalecharacterizationofMarkovprocesses.
484.
4PricingoptionsforMarkov-modulatedsecuritymarkets514.
4.
1IncompletenessofMarkov-modulatedBrowniansecuritymarkets514.
4.
2TheBlack-ScholesformulaforpricingoptionsinaMarkov-modulatedBrownianmarket.
534.
5PricingoptionsforMarkov-modulatedBrownianmarketswithjumps584.
5.
1IncompletenessofMarkov-modulatedBrownian(B,S)-securitymarketswithjumps584.
5.
2Black-ScholesformulaforpricingoptionsinMarkov-modulatedBrownian(B,S)-securitymarketwithjumps604.
6PricingofVariancevswapsforstochasticvolatilitydrivenbyMarkovprocess624.
6.
1StochasticvolatilitydrivenbyMarkovprocess624.
6.
2PricingofvarianceswapsforstochasticvolatilitydrivenbyMarkovprocess634.
6.
3Exampleofvarianceswapforstochasticvolatilitydrivenbytwo-statecontinuousMarkovchain.
64ASomeauxiliaryresults.
64A.
1AFeynmann-KacformulafortheMarkov-modulatedprocess(ys(t),xs(t))t≥s64A.
2FormulafortheoptionpricefT(ST)forthemarketcombinedMarkov-modulated(B,S)-securitymarketandcompoundgeometricPoissonprocess(seeSection4.
4.
2)66References67ContentsVII5SmoothedParameterEstimationforaHiddenMarkovModelofCreditQualityMalgorzataW.
Korolkiewicz,RobertJ.
Elliott695.
1Introduction695.
2DynamicsoftheMarkovchainandobservations705.
3Referenceprobability715.
4Recursivelter715.
5Parameterestimates725.
6Smoothedestimates75AAppendix80References906ExpectedShortfallUnderaModelWithMarketandCreditRisksKinBongSiu,HailiangYang916.
1Introduction916.
2Markovregime-switchingmodel946.
3WeakMarkov-regimeswitchingmodel.
986.
4Concludingremarks99References997FilteringofHiddenWeakMarkovChain-DiscreteRangeObservationsShangzhenLuo,AllanusH.
Tsoi1017.
1Introduction1017.
2BasicSettings.
1037.
3ChangeofMeasure1057.
4Ageneralunnormalizedrecursivelter1077.
5Estimationofstates,transitionsandoccupationtimes1097.
5.
1Stateestimation.
1097.
5.
2Estimatorsforthenumberofjumps1097.
5.
3Estimatorsfor1-stateoccupationtimes1107.
5.
4Estimatorsfor2-stateoccupationtimes1117.
5.
5Estimatorsforstatetoobservationtransitions1117.
6Parameterre-estimations1127.
7Erroranalysis1167.
8Conclusion117References1188FilteringofaPartiallyObservedInventorySystemLakhdarAggoun1218.
1Introduction1218.
2Modeldescription1238.
3Referenceprobability1248.
4Filtering1258.
5FiltersforGmin,andSin128VIIIContents8.
6Parameterre-estimation131References1319AnempiricalinvestigationoftheunbiasedforwardexchangeratehypothesisinaregimeswitchingmarketEmilioRusso,FabioSpagnoloandRogemarMamon1339.
1Introduction1349.
2Stylisedfeaturesandstatisticalpropertiesofforeignexchangerates1359.
3Stationaryandnonstationarytimeseries1399.
4Cointegrationandtheunbiasedforwardexchangerate(UFER)hypothesis1429.
5EvidencefromexchangeratemarketviaaMarkovregime-switchingmodel1469.
6Concludingremarks151References15110EarlyWarningSystemsforCurrencyCrises:ARegime-SwitchingApproachAbdulAbiad15510.
1Introduction15510.
2AMarkov-switchingapproachtoearlywarningsystems15910.
3Datadescriptionandtransformation16210.
4Estimationresults16810.
4.
1Indonesia16810.
4.
2Korea17010.
4.
3Malaysia17010.
4.
4ThePhilippines17110.
4.
5Thailand17510.
5Forecastassessment.
17610.
6Conclusions.
180References182ListofContributorsAbdulAbiadInternationalMonetaryFund70019thSt.
NW,Washington,DC20431USAaabiad@imf.
orgLakhdarAggounDepartmentofMathematicsandStatisticsSultanQaboosUniversityP.
O.
Box36,Al-Khod123,SultanateofOmanlaggoun@squ.
edu.
omRobertJ.
ElliottHaskayneSchoolofBusinessUniversityofCalgary2500UniversityDriveNW,Calgary,Alberta,CanadaT2N1N4relliott@ucalgary.
caMalgorzataW.
KorolkiewiczSchoolofMathematicsandStatisticsUniversityofSouthAustraliaAdelaide,SouthAustralia5095malgorzata.
korolkiewicz@unisa.
edu.
auShangzhenLuoDepartmentofMathematics,UniversityofNorthernIowaCedarFalls,IA50614-0506USAluos@uni.
eduRogemarS.
MamonDepartmentofStatisticalandActuarialSciencesTheUniversityofWesternOntarioLondon,Ontario,CanadaN6A5B7rmamon@stats.
uwo.
caEmilioRussoDepartmentofMathematics,Statis-tics,Computing&ApplicationsandFacultyofEconomicsandBusinessAdministrationUniversityofBergamoviaSalvecchio19,24129Bergamo,Italyemilio.
russo@unibg.
itKinBongSiuDepartmentofStatisticsandActuarialScienceTheUniversityofHongKongPokfulamRoad,HongKongh0010297@hkusua.
hku.
hkXListofContributorsTakKuenSiuDepartmentofActuarialMathemat-icsandStatisticsSchoolofMathematicalandComputerSciences,Heriot-WattUniversity,Edinburgh,UKEH144AST.
K.
Siu@ma.
hw.
ac.
ukFabioSpagnoloCARISMA,BusinessSchoolBrunelUniversity,Uxbridge,UKUB83PHFabio.
Spagnolo@brunel.
ac.
ukAnatolyV.
SwishchukDepartmentofMathematicsandStatisticsUniversityofCalgary2500UniversityDriveNW,Calgary,Alberta,CanadaT2N1N4aswish@math.
ucalgary.
caAllanusH.
TsoiDepartmentofMathematicsUniversityofMissouriColumbia,Missouri65211USAtsoi@math.
missouri.
eduCraigA.
WilsonCollegeofCommerceUniversityofSaskatchewanSaskatoon,Saskatchewan,CanadaS7N5A7cwilson@commerce.
usask.
caShuWuDepartmentofEconomicstheUniversityofKansasLawrence,KS66045,USAshuwu@ku.
eduHailiangYangDepartmentofStatisticsandActuarialScienceTheUniversityofHongKongPokfulamRoad,HongKonghlyang@hkusua.
hku.
hkYongZengDepartmentofMathematicsandStatisticsUniversityofMissouriatKansasCityKansasCity,MO64110,USAzeng@mendota.
umkc.
eduBiographicalNotesEditorsRogemarS.
MamonispresentlyafacultymemberoftheDepartmentofStatisticalandActuarialSciencesattheUniversityofWesternOntario(UWO),London,Ontario,Canada.
PriortojoiningUWOhewasResearchLecturerBinFinancialEngineeringatBrunelUniversity,WestLondon,Eng-land;AssistantProfessorofStatisticsattheUniversityofBritishColumbia;andAssistantProfessorofStatisticsandActuarialScienceattheUniversityofWaterloo.
Hispublicationshaveappearedinvariouspeer-reviewedjournalsinstatistics,appliedmathematics,quantitativenanceandmathematicaled-ucation.
HeisaRegisteredPractitioneroftheHigherEducationAcademyUK,aCharteredMathematicianoftheInstituteofMathematicsanditsAp-plications,andaCharteredScientistoftheUKScienceCouncil.
RobertElliottistheRBCFinancialGroupProfessorofFinanceattheUniversityofCalgary,Canada.
Hehasauthoredandco-authoredmorethan300refereedarticlescoveringthesubjectofharmonicandfunctionalanaly-sis,hypoellipticoperator,dierentialgames,stochasticcalculusandcontrol,stochasticlteringtheoryandmorerecently,quantitativenance.
Hiswell-knownbooksincludeStochasticCalculus(1982),aSpringer-Verlaggraduatetext;HiddenMarkovModels:EstimationandControl(1994)publishedbySpringer-Verlag,co-authoredwithL.
AggounandB.
Moore;MeasureTheoryandFiltering(2004),publishedbyCambridgeUniversityPress,co-authoredwithL.
Aggoun;MathematicsofFinancialMarkets,1sted.
,1999,2nded.
,2005publishedbySpringer-Verlag,co-authoredwithP.
Kopp;andBinomialMethodsinFinance(2005)publishedbySpringer-Verlag,co-authoredwithJohnvanderHoek.
HeheldpreviousacademicpositionsatNewcastle-upon-Tyne,Oxford,WarwickandHullintheUK;Yale,Northwestern,andBrownintheUSA;andAdelaideinAustralia.
HeisaProfessorEmeritusinMath-ematicsandheldtheAFCollinsProfessorialChairinFinancefrom1999toXIIBiographicalNotes2002attheUniversityofAlberta.
HereceivedrstclassBAandMAdegreesfromOxfordandPhDandDScdegreesfromCambridge.
ContributorsAbdulAbiadisanEconomistintheEuropeanDepartmentoftheInter-nationalMonetaryFund(IMF).
HewaspreviouslywiththeIMF'sResearchDepartment,whereheworkedonearlywarningsystemsforcurrencycrises,aswellasonissuesrelatingtothenancialsector.
HehasaPhDfromtheUniversityofPennsylvania,wherehisdissertationfocusedontheapplicationofMarkovmodelstoearlywarningsystemsforcurrencycrises.
LakhdarAggounisanAssociateProfessorofAppliedProbabilityatSultanQaboosUniversity,Oman.
Hehaspublishedseveralarticlesinlteringandcontroltheory.
Heisaco-authoroftwobookswithRobertElliottpublishedbySpringer-VerlagandCambridgeUniversityPress.
HeholdsaB.
Sc.
inMath-ematicsfromtheUniversityofConstantine,Algeria;anMScinMathematicsfromStevensInstituteofTechnology,USA;andanMScinProbabilityandaPhDinAppliedProbabilitybothfromtheUniversityofAlberta,Canada.
MalgorzataKorolkiewicziscurrentlyaLecturerattheSchoolofMathe-maticsandStatisticsandaResearcherattheCentreforIndustrialandAp-pliedMathematicsattheUniversityofSouthAustralia.
Herresearchinterestsincludemathematicalnance,derivativesmarketsandcreditrisk.
ShereceivedherPhDfromtheUniversityofAlberta,Canada.
ShangzhenLuoisanAssistantProfessorintheDepartmentofMathematicsattheUniversityofNorthernIowa(UNI).
HejoinedtheUNIfacultyaftercom-pletinghisPh.
D.
inmathematicsfromtheUniversityofMissouri-Columbia.
HereceivedhisM.
Phil.
degreeinmathematicsfromHongKongUniversityofScienceandTechnologyandB.
S.
inmathematicsfromNankaiUniversity.
HisresearchinterestsincludehiddenMarkovmodels,stochasticcontrol,classicalrisktheoryandtheirapplicationstonanceandinsurance.
EmilioRussoiscurrentlyaPhDstudentattheUniversityofBergamo,Italy.
Hismainareaofinterestsareoptionpricing,optimalassetallocationincontinuousanddiscretetime,insurancepoliciesandmodellinginterestandexchangerates.
HeholdsanMPhilinmathematicalnancefromBrunelUni-versity,UKandbachelour'sdegreeinstatisticsandactuarialsciencesfromtheUniversityofCalabria,Italy.
HehassomepublicationsintheeldofBiographicalNotesXIIIoptionpricingandassetallocation.
Recently,heisworkingonvaluationmod-elsforequity-linkedinsurancepoliciesaspartofhisdoctoraldissertationonthesubjectofcomputationalmethodsineconomics,nancialdecisionsandforecasting.
BonnyK.
B.
Siuisapart-timegraduatestudentattheDepartmentofStatisticsandActuarialScienceoftheUniversityofHongKong,andisaCustomerAnalyticsAssistantManagerinHongKongandShanghaiBankingCorporation(HSBC).
Duringthelastfewyearshehasbeeninvolvedinmanymarketingsalescampaignsandcustomerrelationshipmanagementsystemde-velopmentintheAsia-Pacicregionandiscurrentlylocatedatthecompany'sHongKongheadoce.
Hismainareaofinterestiscreditriskmodelling.
TakKuenSiuisaLecturerinactuarialmathematicsintheDepartmentofActuarialMathematicsandStatisticsatHeriot-WattUniversity,Scotland,whereheteachescoursesinlifeinsurancemathematicsandnancialmathe-matics.
Hisresearchinterestsaremathematicalnanceandactuarialsciencewithspecialisationinriskmeasurementandmanagement,actuarialmethodsforpricingderivativesandinsuranceproducts,creditriskmodelsandnancialtimeseriesanalysis.
Hehaspublishedresearchpapersininternationalrefer-eedacademicandprofessionaljournalsinactuarialscienceandmathematicalnance,includingInsurance:MathematicsandEconomics,NorthAmericanActuarialJournal,QuantitativeFinance,RiskMagazine,InternationalJour-nalofTheoreticalandAppliedFinanceandAppliedMathematicalFinance.
HereceivedhisBScinmathematicsfromHongKongUniversityofScienceandTechnologyin1998andPhDinstatisticsandactuarialsciencefromtheUniversityofHongKongin2001.
FabioSpagnoloisaReaderinFinanceatBrunelBusinessSchool,UK.
HehaspublishedoveradozenofarticlesintheareaofeconometricsandnanceinacademicjournalsincludingEconomicsLetters,JournalofAppliedEconometrics,JournalofEconometrics,JournalofForecastingandStudiesinNonlinearDynamics&Econometrics.
AnatoliySwishchukisanAssistantProfessorofMathematicalFinanceattheUniversityofCalgary,Canada.
Hisresearchinterestsincludethemod-ellingandpricingofvariousswaps,optionpricing,regime-switchingmodelsandstochasticmodelswithdelayinnance.
Heistheauthorofmanyre-searchpapersand8books.
HereceivedhisPhDandDScfromtheInstituteofMathematics,Kiev,Ukraine.
AllanusTsoiobtainedhisBScattheUniversityofWashington,hisM.
Sc.
attheUniversityofIllinoisatUrbana-Champaign,andhisPh.
D.
attheUniver-sityofAlberta,Canada.
HisresearchareainmathematicalnanceincludesAmericanoptionsandAsianoptions,stochasticvolatilitydynamicsandesti-mation,nancialapplicationsofhiddenMarkovlteringtechniques,modellingtermstructureofstochasticinterestratesandanalysisoftheirderivatives,asXIVBiographicalNoteswellasnancialapplicationsofwhitenoisetheory.
HeisatpresentanAs-sociateProfessorofMathematicsattheUniversityofMissouriatColumbia,USA.
Heplayedanessentialroleinsettingupthemathematicalnancepro-gramattheUniversityofMissouri-Columbia.
CraigWilsonisanAssociateProfessorofFinanceattheUniversityofSaskatchewan,Canada.
Heresearchesintheareasofxedincomesecurities,assetpricing,andnancialinvestments.
Inparticular,hecombinesmethodsfromthetheoryofstochasticprocessesandeconometricstomodelandanalysenancialsituations.
HereceivedhisBScinmathematics,BCominnance,andPhDinnancedegreesfromtheUniversityofAlberta,Canada.
ShuWuisanAssistantProfessorandOswaldScholarintheDepartmentofEconomicsattheUniversityofKansas.
Hismainresearchareasaremacroeco-nomicsandnance.
HehaspublishedintheJournalofMonetaryEconomics,JournalofMoney,CreditandBanking,MacroeconomicDynamics,AnnalsofFinanceandInternationalJournalofTheoreticalandAppliedFinance,amongstothers.
HereceivedhisPhDfromStanfordUniversityin2000.
HailiangYangisanAssociateProfessorintheDepartmentofStatisticsandActuarialScienceoftheUniversityofHongKong.
Hiscurrentresearchinter-estsareactuarialscienceandmathematicalnance.
Hehaspublishedover80papersonactuarialscience,mathematicalnanceandstochasticcontrolinacademicjournalsincludingMathematicalFinance,ASTINBulletin,Insur-ance:MathematicsandEconomics,ScandinavianActuarialJournal,Stochas-ticProcessesandtheirApplications,JournalofAppliedProbability,AdvancesofAppliedProbabilityandIEEETransactionsonAutomaticControl.
HeisanassociateeditorofInsurance:MathematicsandEconomics.
HereceivedhisPhDfromtheUniversityofAlberta,Canada.
YongZengisanAssociateProfessorintheDepartmentofMathematicsandStatisticsattheUniversityofMissouri,KansasCity.
Heisavisitingasso-ciateprofessorattheUniversityofTennesseeatKnoxville(Fall2006)andPrincetonUniversity(Spring2007).
HewasalsoaninvitedvisitingscholarinWayneStateUniversity,UniversityofWisconsin-MadisonandUniversityofAlberta.
Hisresearchinterestsincludemarkedpointprocesses;Bayesianinference(estimation,hypothesistestingandmodelselection)vialteringofultra-highfrequencydata,lteringwithmarkedpointprocessobservations,andparticleltering;modellingandestimatingthetermstructureofinter-estrateswithregime-switchingrisks;MLEandMCMCforjumpdiusionprocesswithdiscreteobservations;andstatisticalmodellingfornetworktraf-cdata.
HereceivedhisBSdegreefromFudanUniversity(Shanghai,China)in1990,MSfromtheUniversityofGeorgiaatAthensin1994,andPh.
D.
fromUniversityofWisconsinatMadisonin1999;alldegreesareinstatistics.
PrefaceThetermhiddenMarkovmodel(HMM)ismorefamiliarinthespeechsignalprocessingcommunityandcommunicationsystemsbutrecentlyitisgainingacceptanceinnance,economicsandmanagementscience.
ThetermHMMisfrequentlyrestrictedtomodelswithstatesandmeasurementsinadiscretesetandindiscretetime.
However,thereisnoreasonwhytheserestrictionscannotberelaxed,andsoonecanextendthemodellingincontinuoustimeandincludeobservationswithcontinuousrange.
ThetheoryofHMMdealswithestimation,whichinvolvessignalltering,modelparameteridentica-tion,stateestimation,signalsmoothing,andsignalprediction;andcontrol,whichreferstoselectingactionswhicheectthesignal-generatingsysteminsuchawayastoachievecertaincontrolobjectives.
IntheHMMimplementa-tion,referenceprobabilitymethodsareemployed.
Thisisasetofproceduresdesignedinthereformulationoftheoriginalestimationandcontroltaskinactitiousworldsothatwell-knownresultsforidenticallyandindependentdis-tributedrandomvariablescanbeapplied.
Thentheresultsarereinterpretedbacktotherealworldwiththeoriginalprobabilitymeasure.
TogetabetterunderstandingofanHMM,consideramessagesequenceXk(k=1,2,consistingof0'sand1'sdepictedinFigure1.
Then,possiblythebinarysignalX(aMarkovchain)istransmittedonanoisycommunica-tionschannelsuchasaradiochannelandtheadditivenoiseisillustratedinFigure2.
Whenthesignalisdetectedatthereceiver,weobtainsomeresultantYk.
WhatwegetthereforeaftercombiningFigures1and2isabinaryMarkovchainhiddeninnoisegiveninFigure3.
Essentially,thegoalistodevelopoptimalestimationalgorithmsforHMMstolterouttherandomnoiseinthebestpossibleway.
HMMlteringtheory,therefore,discussestheoptimalrecursiveestimationofanoisysignalgivenasequenceofobservations.
Inelectricalengineeringforexample,oneisinter-estedtodeterminethechargeQ(t),attimetataxedpointinanelectriccircuit.
However,duetoerrorinthemeasurementofQ(s),(sTheobjectiveistoXVIPrefaceFig.
1.
MarkovChainFig.
2.
NoiseFig.
3.
NoisyObservationsY(k)"lter"thenoiseoutofourobservations.
Inasimilarmanner,wemightaskwhethernancialdata,interestrates,assetpriceprocesses,exchangerates,commodityprices,etc.
containinformationaboutlatentvariables.
Ifso,howmighttheirbehaviouringeneralandinparticulartheirdynamicsbeesti-matedTheuseofHMMsisalsomotivatedbysignicantempiricalevidencefromtheliteraturethatfavoursandendorsesMarkov-switchingmodelsinthestudyofmanymacroeconomicvariables.
Thisprovidesmoreexibilitytonancialmodelsandincorporatesstochasticvolatilityinasimpleway.
Earlierdevel-opmentinthisareaduringthelate80'swithinthetimeseriescontextwaspioneeredbyJamesHamilton,amongstothers,inaworkthatproposedtohavetheunobservedregimefollowaMarkovprocess.
Indeed,examplesofPrefaceXVIImanymodelsinwhichtheshiftofregimesisgovernedbyadiscreteorcon-tinuoustimeMarkovchainaboundinnanceandeconomicsintheareasofbusinesscycles,stockprices,foreignexchange,interestratesandoptionvalua-tion.
Therationalebehindtheregime-switchingframeworkisthatthemarketmayswitchfromtimetotimebetween,say,a"quiet"(stablelowvolatility)stateanda"turbulent"(unstablehighvolatility)state.
IngeneraltheMarkovchainstatescanrefertoanynumberofconceivable"stateoftheeconomy".
WithintheHMMset-upandrelatedmodellingstructures,thismonographof-fersacollectionofpapersdealingwiththetheoryandempiricalinvestigationsprobingtheparticularaspectsofdynamicnancialandeconomicmodellingoutlinedabove.
Themainthemesinthiscollectionincludepricing,riskman-agement,modelcalibrationandparameterestimation.
Thisvolumeopenswithtwopapersdevotedtotermstructureofinterestrates.
In'Anexactsolutionofthetermstructureofinterestrateunderregime-switchingrisk',ShuWuandYongZengderiveaclosed-formsolutiontothetermstructureunderanessentiallyane-typemodelusinglog-linearapprox-imation.
Itisshownthatthemarketpriceofregime-switchingriskaectsthelong-endoftheyieldcurveandhencethisisasignicantcomponentofthetermpremiumforlong-termbonds.
ThenRobertElliottandCraigWilsonin'ThetermstructureofinterestratesinahiddenMarkovsetting',developaninterestratemodelwherebythestochasticnatureofvolatilityandmeanre-versionisintroducedinasimpleandtractableway.
Zero-couponbondpriceiscalculated.
Empiricalworkusingnon-linearregressionmodelillustratesthata3-stateMarkovchainisabletoexplainconsiderablythedynamicsoftheyieldratedata.
ThethemeofHMMregime-switching-basedmodelscontinuewithTakKuenSiu'spaperthatdemonstratestheinterplayofmethodologiesinnanceandactuarialsciencetosuccessfullypriceinsuranceproductswithrecentinno-vations.
In'OnFairvaluationofparticipatinglifeinsurancepolicieswithregimeswitching',heemploysaregime-switchingEsschertransformtovalueinsurancepolicieswithembeddedexoticfeatures.
ThevaluationisperformedwithinthebasicgeometricBrownianmotionmodelbutwhosedriftandvolatil-ityparametersaremodulatedbyahiddenMarkovmodel.
Underthesamemarketframework,RobertElliottandAnatoliySwishchukinvestigatethevaluationofoptionsandvarianceswaps.
Twocontributionsthentacklethemeasurementandmanagementofnancialrisks.
In'SmoothedparameterestimationforahiddenMarkovmodelofcreditquality',MalgorzataKorolkiewiczandRobertElliottproposeamodelfortheevolutionofcompanies'creditratingusingahiddenMarkovchainindiscretetime.
SmoothestimatesforthestateoftheMarkovchainandauxiliarypa-rametersarealsoobtained.
KimBongSiuandHailangYang,in'Expectedshortfallunderamodelwithmarketandcreditrisks',presentanintegratedmodelthathandlebothcreditandmarketrisks.
Twoapproachesincalcu-XVIIIPrefacelatingVaRandESaregiven:recursiveequationsandMonteCarlomethods.
AweakMarkovchainmodelisalsooutlinedintheirattempttotakeintoaccountthedependencyofrisks.
ThisisfollowedbypapersonthelteringofHMMviachangeofprobabilitymeasures.
Thedevelopmentofgeneralltersforthestate,occupationtimeandtotalnumberofjumpsofaweakMarkovchainisexaminedbyShangzhenLuoandAllanusTsoiintheirarticle'FilteringofhiddenweakMarkovchain-discreterangeobservations'.
WeakMarkovchainsmaybesuitableinmod-ellingnancialandeconomicprocessesthatexhibitsomeformofmemory.
ThestudyoffuturedemandsandinventorylevelviaadiscreteHMMindis-cretetimeisthefocusofLakhdarAggoun'spaper'Filteringofapartiallyobservedinventorysystem'.
Therecursiveestimationofthejointdistributionofthelevelofstockandactualdemandtogetherwiththere-estimationofmodelparametersishighlighted.
Themonographculminateswithtwopapersthatexploreathought-provokinghypothesisandchallengingquestionsineconomics.
EmilioRusso,FabioSpag-noloandRogemarSMamon,in'Anempiricalinvestigationoftheunbi-asedforwardexchangeratehypothesisinaregime-switchingmarket',useaMarkovchaintodescribestructuralchangebroughtaboutbytheinter-ventionofcentralbanksandotherchangesinthemonetarypoliciesaswellastestthevalidityoftheunbiasedforwardexchangeratehypothesisusingUSdollar/UKsterlingpoundexchangeratedata.
AbdulAbiadputforwardtheuseofMarkovregime-switchingmodeltoidentifyandcharacterisecur-rencycrisisperiods.
In'Earlywarningsystems(EWS)forcurrencycrises:Aregime-switchingapproach',heprovidesempiricalsupportthataregime-switchingmodeloutperformsstandardEWSinsignalingcrisesandreducingfalsealarms.
Country-by-countryanalysesofdatafortheperiod1972-1999fromveAsiancountries(Indonesia,Korea,Malaysia,thePhilippinesandThailand),allofwhichexperiencedcurrencycrises,wereconducted.
Wehopethatthismonographwillprovidemoreinsightstothenancialre-searchcommunityandopenavenuesformoreinterestingproblems.
Speci-cally,itisourhopethatthisvolumewillraisemorestimulatingquestionsforfurtherdiscussionsinourconcertedeorttobuilddynamicmodelsthatcouldincorporatetheimportantstylisedfeaturesofanancialmarketandcapturebetterthesignicantfactorsofaneconomy.
RogemarS.
Mamon(UniversityofWesternOntario)RobertJ.
Elliott(UniversityofCalgary)PrefaceXIXAcknowledgement.
RogemarMamonacknowledgesgratefullythenancialsupportreceivedfromtheBritishAcademy(GrantNo.
OCG-41559),BrunelUniversity(BRIEFAwardNo.
735)andtheFacultyofScience,UniversityofWesternOn-tario.
RobertElliottwishestothanktheSocialSciencesandHumanitiesResearchCouncilofCanadaforthesupportofhisresearch.
ThehelpandexpertiseofPhDcandidateLukaJalen(BrunelUniversity,UK)inproducingconsistentlatexleshavebeenremarkableandinvaluable.
SpecialthanksgotoProfessorGautamMitraforinitiatingtheideaofworkingonthemainsubjectofthismonographandforhissupportinmakingthisprojectmaterialised.
Finally,botheditorswouldliketoexpresstheirsincereappreciationforthesuperbassistanceofFredHillier,GaryFolven,TraceyHowardandCarolynFord,allatSpringer,intheproductionofthismonograph.